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raycasting: how to properly apply a projection matrix?
https://stackoverflow.com/questions/2354821/raycasting-how-to-properly-apply-a-projection-matrix
r = w / h t = tan ( fov_y / 2 ); 2 * n / (r-l) = 1 / (t * a) 2 * n / (t-b) = 1 / t. If the projection is symmetric, where the line of sight is in the center of the view port and the field of view is not displaced, then the matrix can be simplified: 1/ (t*a) 0 0 0 0 1/t 0 0 0 0 - (f+n)/ (f-n) -1 0 0 …
The Perspective and Orthographic Projection Matrix
https://www.scratchapixel.com/lessons/3d-basic-rendering/perspective-and-orthographic-projection-matrix
Ray transfer matrix analysis - Wikipedia
https://en.wikipedia.org/wiki/Ray_transfer_matrix_analysis
Ray-Tracing: Generating Camera Rays (Definition of a Ray)
https://www.scratchapixel.com/lessons/3d-basic-rendering/ray-tracing-generating-camera-rays
Confused Regarding World View Projection Matrix …
https://stackoverflow.com/questions/6849380/confused-regarding-world-view-projection-matrix-question-for-ray-tracing-using-x
for each x pixel do for each y pixel do //Generate Ray //1 - Calculate world coordinates of current pixel //1.1 Calculate Normalized Device coordinates for current pixel 1- to -1 (u, v) u = (2*x/ WIDTH) - 1 ; v = (2*y/HEIGHT) - 1 ; Vector3 rayDirection = -1*focalLength + u'*u + …
Ray Tracing Basics I
http://cs.rit.edu/~jmg/courses/cgII/20072/slides/2-2-raytraceBasics1.pdf
Ray Tracing through the Camera Issues Ray Geometry Object-Ray Intersection Projection Introducing Ray Use mathematical description of a ray and objects to determine intersection. Parametric representation of a ray: Origin of ray, P o = (x o,y o,z o) Direction D = (dx, dy, dz) Ray (ω) = P o + ω D If D is normalized, then ω will be the
Ray tracing algorithm Plane projection in drawing
https://www.cs.cornell.edu/courses/cs465/2007fa/stuff/03raytracing1_F07.pdf
– what objects are created for every ray? try to find a place for them where you can reuse them. – Shadow rays can be cheaper (any intersection will do, don’t need closest)
Applied Mathematics of Ray Tracing and Perspective …
https://www.cureus.com/articles/30351-applied-mathematics-of-ray-tracing-and-perspective-projection-in-fiducial-based-registration-of-x-ray-images.pdf
In PP, a projection matrix can be generated using knowledge of 3D points (fiducials) combined with their associated position on the display plane. A non-skew PP matrix signifies that the angle (theta) is 90 degrees. Coordinates are thought of as 3D (x,y,z) in Step 1, then in Step 2 are still 3D for RT (x,y,z) or PP (u,v,t).
Overview: Ray Tracing & The Perspective Projection Pipeline
https://www.cs.colostate.edu/~cs410/yr2014fa/more_progress/L02_Overview.pdf
Ray Tracing (VI) Step #6: Sum reflections, store in pixel Add together diffuse, specular and translucent reflections, store resulting (R,G,B) value in pixel I=KI l (N⋅L l)+kI l ((2N(N⋅L)−L)⋅V) (n) l ∑ Relax, we will come back to this properly later 8/28/14 © Ross Beveridge & Bruce A. Draper, 2014 17 Ray Tracing (VII)
Homework #2 Shading, Projections, Texture Mapping, Ray …
https://courses.cs.washington.edu/courses/csep557/16au/assets/homework/16au_hw2.pdf
projection plane (PP) is the plane z = zP (note zP is a negative number), so that the distance from COP1 to PP is d = -zP, as shown in the figure below. Let there be two points in the scene, P = [0 yP zP 1]T and Q = [0 yP 2zP 1]T. The projection matrix for this camera is 1000 01 0 0 001/ 0zp
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